In finding the minimum thickness for a thin-walled cylinder,should I use the tangential stress equation or the longitudinal stress equation? How about for maximum thickness?
To determine the minimum thickness for a thin-walled cylinder, you need to consider both the tangential stress and the longitudinal stress equations. The same applies to finding the maximum thickness.
Tangential stress (also known as hoop stress) is the stress acting circumferentially around the cylinder's wall. It is calculated using the equation:
σ_t = (P * r) / t
where:
- σ_t is the tangential stress
- P is the internal pressure applied to the cylinder
- r is the radius of the cylinder
- t is the thickness of the cylinder wall
Longitudinal stress refers to the stress acting along the length of the cylinder. It is calculated using the equation:
σ_l = (P * r) / (2 * t)
where:
- σ_l is the longitudinal stress
The minimum thickness should be determined by the equation that produces the highest stress value. Therefore, compare the values of σ_t and σ_l. The equation that yields the higher stress value indicates the critical stress, which determines the minimum thickness required for structural integrity.
Similarly, for finding the maximum thickness, compare the stress values obtained from both equations. The equation that yields the lower stress value indicates the maximum thickness that can be safely employed.
Keep in mind that these formulas assume certain simplifications and assumptions, such as perfect symmetry, negligible external loads, and uniform wall thickness. It is important to consider the particular requirements and constraints of your specific application to ensure accurate calculations.